Uniform Convergence of the Spectral Expansion for a Differential Operator with Periodic Matrix Coefficients. (29th July 2008)

• Record Type: Journal Article
• Authors: Veliev, O. A.
• Other Names: Abdulla Ugur Academic Editor.
• Is Part Of: Boundary value problems. Volume 2008(2008)
• Publication Date: 2008-07-29
• Subjects: Boundary value problems -- Periodicals; Boundary value problems; Electronic journals; Periodicals; 515.35
• DOI: 10.1155/2008/628973
• Languages: English
• ISSNs: 1687-2762

Abstract

Abstract : We obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and the quasiperiodic boundary conditions. Using these asymptotic formulas, we find conditions on the coefficients for which the root functions of this operator form a Riesz basis. Then, we obtain the uniformly convergent spectral expansion of the differential operators with the periodic matrix coefficients.